(1) Field of the Invention
The present invention relates to a method and a device to demultiplex a frequency modulated stereo-multiplex signal, in particular to an improvement of the signal to noise ratio of a transmitted audio signal.
(2) Description of Related Art
In fm-broadcasting a stereo-multiplex signal is frequency modulated. The stereo-multiplex signal consists of a stereo-sum signal and a stereo-difference signal. The stereo-difference signal is amplitude modulated with suppressed carrier. To allow a coherent amplitude demodulation of the stereo-difference signal at the receiver, a pilot carrier with half the AM-carrier frequency is added to the stereo-multiplex signal.
The stereo-sum signal and the stereo-difference signal are defined byms(t)=al(t)+ar(t)md(t)=al(t)+ar(t)
The stereo-multiplex signal is defined bymstmux(t)=ms(t)+sin(2 ωpilt)·md(t)+Apil·sin(ωpilt) 
The stereo-multiplex signal is frequency modulated:
            S      FM        ⁡          (      t      )        =            A      FM        ⁢          cos      ⁡              (                                            ω              c                        ⁡                          (              t              )                                +                      Δω            ⁢                                          ∫                                  -                  ∞                                t                            ⁢                                                                    m                    stmux                                    ⁡                                      (                    τ                    )                                                  ⁢                                                                  ⁢                                  ⅆ                  τ                                                                    )            with                ωc: carrier frequency        Δω: frequency deviation        
At the receiver side the frequency modulated stereo-multiplex signal is frequency demodulated and stereo-demultiplexed to calculate the left and right audio signal.
For the stereo demultiplexing, the stereo demultiplexer needs to recover the 2nd harmonic of the pilot carrier. Therefore, a PLL locks to the pilot carrier and generates the 2nd harmonic of the pilot carrier. The 2nd harmonic, that is locked in phase to the pilot carrier is needed for the coherent amplitude demodulation of the stereo-difference signal.
FIG. 10 shows the basic functionality of a state of the art stereo-demultiplexer. For the sake of simplicity the noise nb(t) added to the frequency modulated stereo-multiplex signal SFM(t) on the transmitter side, the receiver side and within the transmission channel is shown to be added to the frequency modulated stereo-multiplex signal SFM(t) by way of an adder 10 just before the frequency demodulator 11 of the stereo-demultiplexer shown in FIG. 10. Therefore, the frequency demodulator 11 outputs a stereo-multiplex signal u(t) that consists of the stereo-multiplex signal mstmux(t) as generated on the transmitter side and additionally an added noise component v(t) that is the frequency demodulated noise signal nb(t). On basis of this stereo-multiplex signal u(t) a PLL-circuit 2 generates the 2nd harmonic of the pilot carrier, i.e. a signal that is in phase to the pilot carrier with twice the frequency of the pilot carrier, which is needed for the coherent amplitude demodulation of the stereo-multiplex signal u(t) to gain the stereo-difference signal ud(t). This coherent amplitude demodulation is performed by way of a demodulator 12 which receives the stereo-multiplex signal u(t) at its first input and the 2nd harmonic of the pilot carrier at its second input. The output signal of the demodulator 12 is input to a filter 9 which outputs the stereo-difference signal ud(t) that consists of the stereo-difference signal md(t) generated at the transmitter side plus an additional noise component vd(t). A stereo-sum signal us(t) comprising the stereo-sum signal ms(t) plus an additional noise component vs(t) is generated by a lowpass filtering of the stereo-multiplex signal u(t) with a lowpass filter 8 that receives the output signal of the frequency demodulator 11. The left audio signal is calculated by an addition of the stereo-sum signal us(t) and the stereo-difference signal ud(t). The right audio signal r(t) is calculated by a subtraction of the stereo-difference signal ud(t) from the stereo-sum signal us(t). The left output channel consists of of the left audio signal l(t) and a noise component vd(t)+vs(t) and the right audio channel consists of the right audio signal r(t) and a noise component vs(t)−vd(t).
Therefore, without consideration of the noise nb(t) introduced in the transmission chain, the stereo-sum signal ms(t) is generated by a lowpass filtering of the stereo-multiplex signal and the stereo-difference signal is generated by a coherent amplitude demodulation of the amplitude modulated stereo-difference signal. The left and right audio signals l(t) and r(t) are calculated by addition and subtraction of the stereo-sum signal and the stereo-difference signal:r(t)=ms(t)−md(t)=(al(t)+ar(t))−(al(t)−ar(t))=2ar(t)l(t)=ms(t)+md(t)=(al(t)+ar(t))+(al(t)−ar(t))=2al(t)
For the calculation of the noise of the frequency demodulated signal the noise at the input of the frequency demodulator is assumed to be zero mean Gaussian noise. FIG. 8 shows the assumed power spectral density of the noise nb(t) at the input of the frequency demodulator. The power spectral density Snbnb(jω) equals to N0/2 from frequencies −ωc−Bn to −ωc+Bn and from frequencies ωc−Bn to ωc+Bn. With N0 being the value of the power spectral density of the noise, ωc being the fm carrier frequency and Bn being the noise bandwidth. It is shown in Kammeyer, Nachrichtenübertragung, ISBN 3-519-16142-7 that the power spectral density of the noise v(t) of the frequency demodulated signal can be calculated to:
            S      vv        ⁡          (              j        ⁢                                  ⁢        ω            )        ≈                    (                  ω                      A            FM                          )            2        ⁢          N      o      
The frequency demodulation performed by the demodulator applies quadratic shaping of the input noise spectrum. FIG. 9 depicts the power spectral density (PSD) Svv(jω) of the demodulator output at high carrier to noise ratios (CNRs). It can be seen that Svv(jω) over the frequency ω has the shape of a parabola.
Due to the quadratic shape of the power spectral density of the noise v(t) at the frequency demodulator output such a stereo-demultiplexer described above in connection with FIG. 10 is not optimal in terms of the noise behavior, since those parts of the spectrum of the modulation signal having a higher frequency are more deteriorated than those with a lower frequency.